Question

The number of 6 digit numbers that can be formed using the digits 1, 3, 5 with the condition that 5 occurs twice in each number, is:

• A. 45
• B. 75
• C. 185
• D. 240

Answer 1

Answer: (D)

240

Answer 2

We have to form a 6 digit number of which two digits must necessarily be 5. The digit 5 can be arranged in $6C_{2}$ ways. Now, for the remaining four places, we have two options, viz., 1, 3 for every place. Thus the remaining places can be filled in 2⁴ ways.

Hence, the required number of ways = $6C_{2}x2^{4}$ = 240 ways.